Document FR-A-2 551 810 describes an example of such a headrest.
Headrests of that type suffer, in particular, from the drawback of increasing the overall size of the seat while said seat is being transported and/or while it is being mounted in the vehicle, when the seat is transported and/or mounted with the headrest mounted on the back of the seat. That increase in overall size complicates and increases the cost of transporting and/or mounting the seat, and it can even be incompatible with mounting the seat in certain small vehicles.